How do you prove Sinx+cosx=1?

1 Answer
José F.
Mar 5, 2016

it is sin^2x+cos^2 x which is equal to 1!

Explanation:

Just imagine any rectangle triangle. Take one of its acute angles.

The sine of this angle is the opposite catet dividing by the hypotenuse (a/h), and the cosins of this angle is the adjacent catet dividing by the hypotenuse (b/h)

So

sin^2x+cos^2 x=(a/h)^2+(b/h)^2= (a^2+b^2)/(h^2)

But by the Pythagoras theorem we know that the sum of the square of the catets (a^2+b^2) it is the square of the hypotenuse:

So (a^2+b^2)/(h^2)=(h^2)/(h^2)=1

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